TS EAMCET · Maths · Matrices
If \(\mathrm{A}\) is a symmetric matrix with real entries, then
- A \(\mathrm{A}^{-1}\) is symmetric, if it exists
- B \(\mathrm{A}^{-1}\) always exists and is symmetric
- C \(\mathrm{A}^{-1}\) is skew symmetric, if it exists
- D \(\mathrm{A}^{-1}\) always exists and is skew-symmetric
Answer & Solution
Correct Answer
(A) \(\mathrm{A}^{-1}\) is symmetric, if it exists
Step-by-step Solution
Detailed explanation
If \(A\) is symmetric then \(A^T=A\) \[ \left(A^{-1}\right)^T=\left(A^T\right)^{-1}=A^{-1} \] \(\therefore \quad A^{-1}\) is also symmetric.
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